Solidarity may be an unfashionable virtue today, but it is the best - and often the only - defence most people have in a world dominated by big money, growing inequality and unrestrained profit-making. May Day has, for over a century, been the day working people have proclaimed their common interests across industries and countries. Its message of the necessity for solidarity is even more decisive than in the past.

There is no shortage of pundits who will tell you this is no more than an exercise in nostalgia and that the working class is all washed up, marginalised, that everyone is out for number one, that workers are just shoppers taking a break from the stores. The reality is different. Our times not only demand but impel a reassertion of our vision of a world of solidarity and social justice, and the evidence is that people will express those values given the chance. Perhaps that is why solidarity within and between workplaces is still illegal in Britain.

Workers in one factory break the law if they walk out in support of those in another threatened with closure, for example. That is why trade unions and more than 100 MPs - as well as today's TUC-backed May Day march in London - are supporting the proposed trade union freedom bill. It would bring solidarity back within the law and help redress the balance of power in the workplace, still set within the framework cast by Margaret Thatcher, by making it harder for employers to break legal strikes.

Changing the law to allow working people to support each other when their interests are challenged, as employers do every day, would be an elementary act of justice. But the labour movement faces other pressing challenges - and we are starting to meet them. My own union, the T&G, has dozens - soon to be more than 100 - of organisers taking trade unionism to workplaces and to a generation that has never known the benefits of collective strength.

Our organisers look like today's working class in this country - many are black, more are women, most are young. Already they have recruited thousands of new members in logistics, in building materials, in food processing, in budget airlines and in contract cleaning, including many migrant workers. Just as important, they have helped train more than 500 new shop stewards - the workplace leaders of the future. Other unions, like PCS in the civil service and RMT on the railways, are doing it too, by putting members' interests first and rejecting the phoney "partnership" approach that did so much damage in the 1990s.

But it needs to be done all around the world as well. Organising in one country has serious limitations in a globalised economy. Capital's power to shift jobs around to maximise profit has been most recently highlighted by Peugeot's plan - in breach of promises - to close its Coventry plant.

Labour will only be able to look capital in the eye when it, too, is organised internationally. We cannot do our job properly if we remain stubbornly national while giant corporations are knitting the interests of workers all over the world together. That is why unions are working across frontiers in taking on companies like food-servicing giants Compass and Sodexho and transport monopoly First Group. Recent successful union campaigns and demonstrations in Brussels and Strasbourg, against EU directives that would have caused devastation for workers in the service sector and in the docks, point in the same direction.

Solidarity must mean something in our communities too. The danger presented by the British National party exploiting for its racist agenda what are, at bottom, the failures of capitalism, is evident. If our rich country could only guarantee stable employment and decent homes for everyone, racism would speedily be pushed to the electoral margins. The failure to do so underpins the alienation from the political process in many working-class communities. We have had enough lectures about the benefits of "labour market flexibility", the wonders of the market, and the unavoidable consequences of globalisation.

That rhetoric leads millions to believe they are powerless to make any difference to their lives. It is reinforced by conventional opinion that treats the working class - the majority of the country - as either unmentionable or politically irrelevant. The signs are that the Labour party recognises the problem. Our conference has voted in recent years for the right to express solidarity, the public ownership of railways, a fair deal for council housing, and an end to creeping NHS privatisation and public finance initiative scams - all against ministerial recommendation.

But the government has ignored those votes and is now paying the price in safe Labour areas. I hope Thursday's local elections go better for Labour than predicted - many Labour councils are doing their best for working people - but if not, real Labour opinion in the party will need to reassert itself.

In recent months, millions have shown they want a different world of greater justice, democracy and equality: in Latin America, the global anti-war movement, and the French workers who defeated the recent attempt to slash labour protection. That world is the ultimate purpose of the union freedom we are demanding today.

· Tony Woodley is general secretary of the Transport and General Workers' Union